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  • ...ot \overrightarrow{w}|</cmath> with equality if and only if there exists a scalar <math>t</math> such that <math>\overrightarrow{v} = t \overrightarrow{w}</m ...n the left-hand side of the inequality is equal to the square of the [[dot product]] of <math>\mathbf{a} </math> and <math> \mathbf{b} </math>, or <math>(\mat
    13 KB (2,048 words) - 14:28, 22 February 2024
  • #<math>1\vec{x}=\vec{x}</math> (Unit scalar identity) #<math>(ab)\vec{x}=a(b\vec{x})</math> ([[Associative]] in scalar)
    11 KB (1,876 words) - 18:01, 29 August 2024
  • ..., d_2 , d_3 ) </math>, then we may rewrite the expression (using [[scalar product | dot products]]) thus:
    2 KB (346 words) - 13:59, 30 July 2006
  • ...that changes in momentum (acceleration) of fluid particles are simply the product of changes in pressure and dissipative viscous forces (similar to friction) ...(which is a vector field), <math>p</math> be the pressure field(which is a scalar), <math>\rho</math> be the density of the fluid, <math>\nu</math> be the ki
    3 KB (553 words) - 21:08, 2 May 2022
  • ..., then the volume of the parallelepiped is the same as the [[scalar triple product]] of the vectors, or <math>a \cdot (b \times c)</math>. Suppose that <math>
    2 KB (248 words) - 19:08, 17 August 2023
  • ...in the numerator, so <math>d=\frac{3\sqrt{3}}{2}</math>. Multiply back the scalar and you get <math>\boxed{450}</math>. Not that hard, was it? ...ath>120^{\circ}</math>, so after solving for the vectors, taking their dot product, equating it to <math>PM \cdot QM \cdot\cos{120^{\circ}}</math>, and <math>
    17 KB (2,861 words) - 18:39, 25 November 2024
  • The product of <math>\nabla</math> and a function <math>f(x_1, x_2, \dots, x_n)</math> The gradient applies when <math>f</math> is a [[scalar]]-valued function of many variables. For example, the gradient of temperatu
    4 KB (734 words) - 19:51, 4 May 2022
  • Scalar product <math>(\vec{B'D} \cdot \vec {HG}) = 0.</math> Find all possible values of the product <math>xy</math> if it is known that <math>x,y \in \left [ 0, \frac{\pi}{2}
    48 KB (8,214 words) - 07:59, 30 July 2024